148 3. THE COMPACTNESS THEOREM FOR RICCI FLOW
- Notes and commentary
Some basic references for compactness theorems for Riemannian metrics
are Cheeger [70], Greene and Wu [165], Gromov [169], and Peters [300].
A survey of compactness theorems in Riemannian geometry has been given
in Petersen [301]..
The compactness theorem for Ricci flow in this chapter was proven by
Hamilton in [187] and was used to classify singularities and nonsingular so-
lutions in [186], [190] and [297]. Cheeger-Gromov theory was also directly
used to study the Ricci flow in Carfora and Marzuoli [57]. Further com-
pactness theorems on the Ricci flow which extend Hamilton's results can be
found in [257] and [156].
It should be noted that there has been much work to ensure the injec-
tivity radius bound for dilations of singularities, most notably by Hamilton
[186] and Perelman [297]. Additional work on injectivity radius estimates
has been done by Wu [372] and by the authors of [112] in the case of
2-dimensional orbifolds and [109] for sequences of solutions with almost
nonnegative curvature operator.